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  "body": "\n## Summary\n\nRobust statistics studies statistical procedures whose results change little when the data depart slightly from the model assumptions.\nSuch departures include outliers or a heavier tail than assumed.\nTwo main measures of robustness are the [[breakdown point|BRGGGZVQDS]] and the [[influence function|EB2QJQNE5Z]].\nThe first says how much bad data an estimator can absorb, and the second how much a single point can move it.\nTypical robust procedures are the median, trimmed means and other [[L-estimators|E3C4F0RKJY]], and Huber's [[M-estimators|4503R8BVF8]].\nThe field was shaped by Tukey, Huber and Hampel from the 1960s on.\n\n## Explanations\n\n### L1 human\n\nThe average of a list of incomes can jump enormously when one billionaire joins the list.\nThe median barely moves.\nRobust statistics prefers methods like the median, which give sensible answers even if a few data points are wrong or extreme.\nIt also studies the price of this safety, since robust methods are often a little less precise when the data really are clean.\n",
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